The following is a table of the total cost (TC) of producing output Q for a particular firm: Q 10 20 30 40 50 60 70 80 90 100 TC (£) 140 210 265 310 360 420 490 570 660 760 Based o... The following is a table of the total cost (TC) of producing output Q for a particular firm: Q 10 20 30 40 50 60 70 80 90 100 TC (£) 140 210 265 310 360 420 490 570 660 760 Based on this information, which of the following statements is incorrect? a. The marginal cost at Q = 80 is £9. b. The marginal cost is lower than the average cost at Q = 50. c. The average cost at Q = 20 is £10.50 d. The marginal cost curve intersects the average cost curve at Q = 50.

Question image

Understand the Problem

The question presents data regarding total costs associated with different output levels for a firm. It asks which of the given statements about marginal cost and average cost based on this data is incorrect.

Answer

The incorrect statement is (d): The marginal cost curve intersects the average cost curve at $Q = 50$.
Answer for screen readers

The incorrect statement is (d): The marginal cost curve intersects the average cost curve at $Q = 50$.

Steps to Solve

  1. Calculate Marginal Cost (MC)

Marginal cost is calculated as the change in total cost divided by the change in quantity produced. For instance, to find the marginal cost from $Q = 70$ to $Q = 80$:

  • Total Cost at $Q = 70$ is £570
  • Total Cost at $Q = 80$ is £660

[ MC = \frac{TC_{80} - TC_{70}}{Q_{80} - Q_{70}} = \frac{660 - 570}{80 - 70} = \frac{90}{10} = £9 ]

  1. Verify Statement a - MC at Q = 80

From the calculation above, the marginal cost at $Q = 80$ is indeed £9, so statement (a) is correct.

  1. Calculate Average Cost (AC) for Q = 50

To find the average cost, divide the total cost by the quantity produced. For $Q = 50$:

  • Total Cost at $Q = 50$ is £360.

[ AC = \frac{TC}{Q} = \frac{360}{50} = £7.20 ]

  1. Calculate Marginal Cost for Q = 50

To find the marginal cost at $Q = 50$, look at the change from $Q = 40$ to $Q = 50$:

  • Total Cost at $Q = 40$ is £310

[ MC = \frac{TC_{50} - TC_{40}}{Q_{50} - Q_{40}} = \frac{360 - 310}{50 - 40} = \frac{50}{10} = £5 ]

  1. Verify Statement b - Compare MC and AC at Q = 50

Here, marginal cost £5 is lower than average cost £7.20, so statement (b) is also correct.

  1. Calculate Average Cost (AC) at Q = 20

To find the average cost for $Q = 20$:

  • Total Cost at $Q = 20$ is £210.

[ AC = \frac{TC}{Q} = \frac{210}{20} = £10.50 ]

  1. Verify Statement c - AC at Q = 20

Since the calculation shows average cost at $Q = 20$ as £10.50, statement (c) is correct.

  1. Check Statement d - Marginal Cost Intersects AC at Q = 50

Marginal cost equals average cost at the minimum point of the average cost curve. Since we've calculated that at $Q = 50$, AC (£7.20) does not equal MC (£5). Therefore, statement (d) must be the incorrect statement as it implies a necessary intersection.

The incorrect statement is (d): The marginal cost curve intersects the average cost curve at $Q = 50$.

More Information

The relationship between marginal cost and average cost is fundamental in economics; MC intersects AC at its minimum point. When MC is below AC, it pulls AC down. Conversely, when MC is above AC, it pulls AC up.

Tips

  • Miscalculating average or marginal cost by not correctly applying the formulas.
  • Confusing where to find marginal cost (change between two total costs) versus average cost (total cost divided by quantity).

AI-generated content may contain errors. Please verify critical information

Thank you for voting!
Use Quizgecko on...
Browser
Browser